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Math Help - Differentiation help please

  1. #1
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    Differentiation help please

    Differentiate

    ln(x)
    ----
    ..x
    Last edited by MathGuru; September 16th 2005 at 09:59 AM.
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  2. #2
    MHF Contributor
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    ln(x)
    ----
    ..x

    = ln(x) / x

    Let y = ln(x) / x
    Differentiate both sides with respect to x,
    dy/dx = {x*[1/x] -ln(x) *[1]} / x^2
    dy/dx = {1 -ln(x)} / x^2

    That is it.

    We used
    d/dx (u/v) = {v*du -u*dv} / v^2
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  3. #3
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    Yes, but as I said in my original post (which seems to have been altered) x=e which changes things significantly, I got as far as you did but I can't get the last part to work out to the right answer.
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  4. #4
    MHF Contributor
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    x = e?

    if so, then
    ln(x) / x
    = ln(e) / e
    = 1/e
    And differentiating that will give you zero because 1/e is a constant.

    ---------
    If you substitute e for x in the derivative dy/dx = {1 -ln(x)} / x^2,
    dy/dx = {1 -ln(e)} / e^2
    dy/dx = {1 -1} / e^2
    dy/dx = {0} / e^2
    dy/dx = 0 ------------------still zero.
    Last edited by ticbol; September 17th 2005 at 04:57 AM.
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